Six angles of a convex octagon is congruent. Each of the two remaining angles is 20 degrees more than one of the other six angles. Find the measure of EACH angle.

Question

asked Jul 26, 2023 14.7k views

1 Answer

LarsC · Answer 1 · 2023-07-31T18:41:03+0000

Determine the sum of angles of octagon.

$\begin{gathered} S=(n-2)*180 \\ =(8-2)*180 \\ =6\cdot180 \\ =1080 \end{gathered}$

Let measure of each angle of six congurent angle be x.

Then measure of each of other two remaining angle is (x + 20).

Determine the value of x by using the sum of angles of octagon.

$\begin{gathered} x+x+x+x+x+x+x+20+x+20=1080 \\ 8x=1080-40 \\ x=(1040)/(8) \\ =130 \end{gathered}$

So measure of each angle of six congurent angle is 130 degree.

Determine the measure of two remaining angles.

$\begin{gathered} x+20=130+20 \\ =150 \end{gathered}$

Thus measure of angles of octagone are,

Six angle measure 130 degree each and two angle measure 150 degree each.